Hyperfine splitting in noncommutative spaces

TL;DR

This paper investigates how noncommutative quantum mechanics affects hyperfine splitting, revealing deviations from standard quantum mechanics and providing bounds on noncommutativity parameters.

Contribution

It analyzes hyperfine splitting within noncommutative quantum mechanics and derives how energy differences and radiation wavelengths are altered compared to conventional theory.

Findings

Energy difference between excited and ground states is larger in noncommutative spaces.

Radiation wavelength in noncommutative spaces is shorter than in commutative spaces.

An upper bound for the noncommutativity parameter is established.

Abstract

We study the hyperfine splitting in the framework of the noncommutative quantum mechanics (NCQM) developed in the literature. The results show deviations from the usual quantum mechanics. We show that the energy difference between two excited F = I + 1/2 and the ground F = I - 1/2 states in a noncommutative space (NCS) is bigger than the one in the commutative case, so the radiation wavelength in NCSs must be shorter than the radiation wavelength in commutative spaces. We also find an upper bound for the noncommutativity parameter.